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A formula for the value of a stochastic game
Luc Attia1, Miquel Oliu-Barton2
1Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France.
Summary
This study introduces a new, practical formula for calculating the value of competitive stochastic games. This advances the theory of game dynamics and decision-making under uncertainty.
Area of Science:
- Game Theory
- Mathematical Economics
- Decision Science
Background:
- The concept of stochastic games was introduced by Lloyd Shapley in 1953, establishing a foundational model for dynamic game interactions.
- Shapley proved that competitive stochastic games possess a discounted value, a key concept in analyzing such systems.
- Mertens and Neyman (1982) later established the robust "value" of these games as the limit of discounted values, a significant advancement in game theory.
Purpose of the Study:
- To derive a tractable formula for the value of competitive stochastic games.
- To provide a practical method for calculating game values, building upon Shapley's and Mertens-Neyman's foundational work.
Main Methods:
- The research focuses on developing a computational formula for the game value.
- The methodology involves advanced mathematical analysis of stochastic game structures.
Main Results:
- A tractable formula for the value of competitive stochastic games has been successfully derived.
- This formula offers a practical approach to determining game values.
Conclusions:
- The development of this tractable formula represents a significant step forward in the practical application of stochastic game theory.
- This work provides a valuable tool for analyzing and understanding complex competitive dynamics.
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